Answer:
-India, Iran, Afghanistan, Myanmar, Sri Lanka, the Marquesas, as well as parts of Australia use half-hour deviations from standard time, and some nations, such as Nepal, and some provinces, such as the Chatham Islands of New Zealand, use quarter-hour deviations.
-This has largely to do with the politics in each of those places. For example, in New Delhi, India, they found themselves halfway between two meridians, and therefore decided to be 30 minutes between each, as opposed to adopting one time or the other
Meridians - a circle of constant longitude passing through a given place on the earth's surface and the terrestrial poles.
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